NumPy Incidence with Integration

Question

I have a vector and want to make another vector of the same length whose kth component

Question: how can we vectorize this for speed? NumPy vectorize () is actually a for loop, so it doesn't count.

Veedrac noted that " It is not possible to apply a pure Python function to each element of a NumPy array without calling it many times ." Since I use NumPy functions and not "pure Python", I assume that this is possible for vectorization, but I do not know how to do this.

import numpy as np
from scipy.integrate import quad
ws = 2 * np.random.random(10) - 1
n  = len(ws)
integrals = np.empty(n)

def f(x, w):
    if w < 0: return np.abs(x * w)
    else:     return np.exp(x) * w

def temp(x): return np.array([f(x, w) for w in ws]).sum()

def integrand(x, w): return f(x, w) * np.log(temp(x))

## Python for loop
for k in range(n):
    integrals[k] = quad(integrand, -1, 1, args = ws[k])[0]

## NumPy vectorize
integrals = np.vectorize(quad)(integrand, -1, 1, args = ws)[0]

On a side note, is a Cython loop always faster than a NumPy vectorization?

Answer 1

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• numpy.trapz
• scipy.integrate.simps ( , ).
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Answer 2

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    else:     return np.exp(x) * w

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